Of course, from a quantum gravity perspective, one would like to escape branched polymers in favour of some continuum metric space that has physically interesting characteristics, as they have done in the causal dynamical triangulations approach to quantum gravity [1]}. In particular, one would like to recover a macroscopic 4-dimensional universe in some limit. Were this possible, then the colored graph approach would have a significant advantage in that one has the bubble Lie algebra (or some subalgebra thereof) at one's disposal, from which one could aim to extract the underlying symmetries of the continuum limit.
